A new deterministic model for the population biology of immature and mature mosquitoes is designed and used to assess the impact of temperature and rainfall on the abundance of mosquitoes in a community. The trivial equilibrium of the model is globally-asymptotically stable when the associated vectorial reproduction number $({\mathcal R}_0)$ is less than unity. In the absence of density-dependence mortality in the larval stage, the autonomous version of the model has a unique and globally-asymptotically stable non-trivial equilibrium whenever $1 < {\mathcal R}_0 < {\mathcal R}_0^C$ (this equilibrium bifurcates into a limit cycle, via a Hopf bifurcation at ${\mathcal R}_0={\mathcal R}_0^C$). Numerical simulations of the weather-driven model, using temperature and rainfall data from three cities in Sub-Saharan Africa (Kwazulu Natal, South Africa; Lagos, Nigeria; and Nairobi, Kenya), show peak mosquito abundance occurring in the cities when the mean monthly temperature and rainfall values lie in the ranges $[22 -25]^{0}$C, $[98 -121]$ mm; $[24 -27]^{0}$C, $[113 -255]$ mm and $[20.5 -21.5]^{0}$C, $[70 -120]$ mm, respectively (thus, mosquito control efforts should be intensified in these cities during the periods when the respective suitable weather ranges are recorded).

K. Berkelhamer and T. J. Bradley,
Mosquito larval development in container habitats: The role of rotting Scirpus californicus, Journal of the American Mosquito Control Association, 5 (1989), 258-260.
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E. Van Handel,
Nutrient accumulation in three mosquitoes during larval development and its effect on young adults, Journal of the American Mosquito Control Association, 4 (1988), 374-376.
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K. Berkelhamer and T. J. Bradley,
Mosquito larval development in container habitats: The role of rotting Scirpus californicus, Journal of the American Mosquito Control Association, 5 (1989), 258-260.
Google Scholar

E. Van Handel,
Nutrient accumulation in three mosquitoes during larval development and its effect on young adults, Journal of the American Mosquito Control Association, 4 (1988), 374-376.
Google Scholar

Figure 3.
Simulations of the autonomous model (6), showing: (a) total number of female adult mosquitoes of type $U(t)$ as a function of time. (b) phase portrait of $U(t) -P(t)$ showing a stable limit cycle. The parameter values used are as given in the simulations for Figure 2 with $\psi_U = 110.91$ and $\mu_A = 0.12$ (so that, $\mathcal{R}_0 = 4.6849 > \mathcal{R}^C_0 = 4.5573$)

Figure 4.
Bifurcation curves in the $\mu_A-$$\psi_U$ plane for the autonomous model (6). The parameter values used are as given in the simulations for Figure 2 with $\psi_U \in [0,6000]$ and $\mu_A \in [0, 0.5]$

Figure 5.
Simulation of model (1), using parameter values in Table 4, showing the total number of female adult mosquitoes ($A_M$) for various values ofmean monthly temperature and rainfall values in the range $T \in [16,40]^\circ$C and $R \in [90,120]$mm

Table 5.
PRCC values for the parameters of the autonomous model (6) using total number of adult mosquitoes of type $U$, adult mosquitoes of type $V$, fourth instar larvae ($L_4$), pupae ($P$), and $\mathcal{R}_0$ as output. The top (most dominant) parameters that affect the dynamics of the model with respect to each of the six response function are highlighted in bold font. "Notation: a line ($-$) indicates the parameter is not in the expression for $\mathcal{R}_0$"